Positive-strand RNA viruses are the largest genetic class of viruses and include many serious human pathogens. All positive-strand RNA viruses replicate their genomes in association with intracellular membrane rearrangements such as single- or double-membrane vesicles. However, the exact sites of RNA synthesis and crucial topological relationships between relevant membranes, vesicle interiors, surrounding lumens, and cytoplasm generally are poorly defined. We applied electron microscope tomography and complementary approaches to flock house virus (FHV)-infected Drosophila cells to provide the first 3-D analysis of such replication complexes. The sole FHV RNA replication factor, protein A, and FHV-specific 5-bromouridine 5'-triphosphate incorporation localized between inner and outer mitochondrial membranes inside approximately 50-nm vesicles (spherules), which thus are FHV-induced compartments for viral RNA synthesis. All such FHV spherules were outer mitochondrial membrane invaginations with interiors connected to the cytoplasm by a necked channel of approximately 10-nm diameter, which is sufficient for ribonucleotide import and product RNA export. Tomographic, biochemical, and other results imply that FHV spherules contain, on average, three RNA replication intermediates and an interior shell of approximately 100 membrane-spanning, self-interacting protein As. The results identify spherules as the site of protein A and nascent RNA accumulation and define spherule topology, dimensions, and stoichiometry to reveal the nature and many details of the organization and function of the FHV RNA replication complex. The resulting insights appear relevant to many other positive-strand RNA viruses and support recently proposed structural and likely evolutionary parallels with retrovirus and double-stranded RNA virus virions.